Compact Representation of Spectral BRDFs Using Fourier Transform and Spherical Harmonic Expansion

• Published in: Computer graphics forum Vol. 25; no. 4; pp. 759 - 775
• Main Authors: Xu, Huiying, Sun, Yinlong
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01-12-2006
• Subjects: Computer graphics; Computer programming; Data compression; E.2 Data Storage Representations; error evaluation; Fourier transform; Fourier transforms; I.3.0 Computer Graphics: General; I.3.6 Computer Graphics: Methodology and Techniques; Normal distribution; representation; spectral BRDFs; spectral rendering; spherical harmonics; Studies
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/j.1467-8659.2006.00997.x

This paper proposes a compact method to represent isotropic spectral BRDFs. In the first step, we perform a Fourier transform in the wavelength dimension. The resulting Fourier coefficients of the same order depend on three angles: the polar angle of the incident light, and the polar and azimuth angles of the outgoing light. In the second step, given an incident light angle, when the Fourier coefficients of the same order have an insensitive dependency on the outgoing direction, we represent these Fourier coefficients using a linear combination of spherical harmonics. Otherwise, we first decompose these Fourier coefficients into a smooth background that corresponds to diffuse component and a sharp lobe that corresponds to specular component. The smooth background is represented using a linear combination of spherical harmonics, and the sharp lobe using a Gaussian function. The representation errors are evaluated using spectral BRDFs obtained from measurement or generated from the Phong model. While maintaining sufficient accuracy, the proposed representation method has achieved data compression over a hundred of times. Examples of spectral rendering using the proposed method are also shown.